Will More grain in a partial mash give more body to my IPA

That depends on how you define "body."

This BYO article offers a pretty solid definition on body:

"Body is the sensation of palate fullness, the viscosity and feel of beer in the mouth. It is a characteristic of beer that reflects its ending density and refers to the mouth-filling and thickness properties that a given sample contains."

The BYO article above goes into greater detail about proteins, starches, and enzymes -- for the sake of simplicity a higher final density, or final gravity, can easily be achieved using the following methods:

1. Utilizing a yeast strain with lower attenuation properties
2. Adding un-fermentable sugars (like lactose) or "body builders" like (like flaked oats, or cara-pils malt) to your brew.

Based on my experience, I would recommend adding cara-pils (maybe 0.5 lb.) to your steeping grains, and use a lower attenuating yeast. Check with your local HBS to see what yeast they have in stock for lower attenuation that meets style.

Best of luck!

It could, but keep in mind that it could also have other effects like reducing fermentability. But adding 1/2 lb. of C40 or C60 or carapils could help the body. Yeast choice also has an influence. Something like WY1450 will leave more mouthfeel in your beer while still giving you good attenuation. A yeast like US-05 will leave you with a thin body.